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We attach to any number field K a universal group K2(K), which is the analogue of the group of symbols K2(K), together with two canonical finite subgroups R2(K) and H2(K) that correspond respectively to the tame and wild kernels of Ktheory. Thanks to them, we establish noteworthy correspondances between classical Galois modules in relation with both Leopoldt and Gross conjectures.

La théorie de Kummer et le $K_2$ des corps de nombres